A160092 Decimal expansion of (617139 + 371510*sqrt(2))/569^2.

3, 5, 2, 8, 9, 4, 1, 0, 4, 1, 5, 6, 2, 2, 2, 8, 1, 2, 9, 9, 4, 8, 6, 8, 2, 4, 4, 7, 6, 4, 2, 3, 8, 1, 0, 5, 6, 3, 0, 2, 0, 8, 3, 3, 2, 2, 0, 2, 2, 3, 8, 6, 8, 1, 8, 2, 5, 7, 5, 0, 5, 6, 5, 8, 3, 7, 4, 3, 4, 7, 1, 9, 7, 6, 9, 6, 6, 2, 6, 1, 7, 1, 7, 8, 5, 0, 7, 4, 4, 0, 0, 1, 8, 4, 2, 7, 8, 2, 8, 1, 4, 6, 9, 3, 0

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Index entries for algebraic numbers, degree 2.

Formula

Equals (1940 + 766*sqrt(2))/(1940 - 766*sqrt(2)).

Equals (3 + 2*sqrt(2))*(34 - 3*sqrt(2))^2/(34 + 3*sqrt(2))^2.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 0, b = A101152.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 1, b = A160090.

Minimal polynomial: 323761*x^2 - 1234278*x + 323761. - Amiram Eldar, May 11 2026

Example

3.52894104156222812994868244764238105630208332202238...

Mathematica

RealDigits[(617139 +371510*Sqrt[2])/569^2, 10, 100][[1]] (* G. C. Greubel, Apr 21 2018 *)

Prog

(PARI) (617139 +371510*sqrt(2))/569^2 \\ G. C. Greubel, Apr 21 2018
(Magma) (617139 +371510*Sqrt(2))/569^2; // G. C. Greubel, Apr 21 2018

Crossrefs

Cf. A101152, A160090, A002193 (decimal expansion of sqrt(2)), A160091 (decimal expansion of (587+102*sqrt(2))/569).

Sequence in context: A095749 A137988 A258367 * A282348 A026193 A026143

Adjacent sequences: A160089 A160090 A160091 * A160093 A160094 A160095

Keyword

cons,nonn

Author

Klaus Brockhaus, May 04 2009

Status

approved